Fwah Ruud: you're torturing me. That is a fantastic puzzle. Had to use a chain move to unlock it. But perhaps someone can find a better way. Found some really interesting ways to use LoL - hope they are valid. Couldn't find a way to use Jean-Christophe's really great use of LoL and cage sums from TJK28 though. Perhaps that's why I found this puzzle so hard.

Won't put the walk-through into tiny text this time. Please let me know of any shortcuts missed, or improvements/corrections. [Thanks to Glyn for some improvements/corrections and naming ][And more improvements and corrections from Andrew. Thanks!]
Enjoy! Ed

21. 16(3)r5c1 = {259/268/349/367} ({358/457} blocked by 8(3)r5c7)
21a. 16(3) = [2/3..], 8(3)r5c7 = [2/3]: Killer pair 2/3: 2 & 3 locked for r5
[Andrew noticed that 45 on r5 3 innies r5c456 = 21 is a simpler way to do the above and I use that "45" in the next step. Thanks]
21b. 2 in n5(r2c1) is either in the innies of LoLr6789 (step 19) -> must be in r5c89 for outies OR 2 in n5 is in 16(3)r5c1.
21c. Either way, no 2 r5c7. Is there a name for this move? ( LoLR - "Law of Left(&Right)-overs")
21d. -> no 5 r5c89 ({125} combo must have 5 in r5c7)
21e. -> no 5 in innies of LoL r6789 (step 19) in r6c12+r7c1 (rest of this step deleted)
21f. no 6 in the outies -> no 6 in innies-> no {156} combo in 12(3)r7c1